Find the value of (2^2 A) for the following matrix: A = 2 & 3 & 1 \\ -1 & 0 & 2 \\ -3 & 1 & 2 - Mathematics MCQ Mathematics Mock Test - 4 2026 | ExamTest.live

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Find the value of det (2^{2} A) for the following matrix: A = 2 - 1 - 3 301122

Solution & Step-by-step Explanation

First, find det (A) : det (A) = 2 (0 - 2) - 3 (- 2 + 6) + 1 (- 1 - 0) det (A) = 2 (- 2) - 3 (4) + 1 (- 1) det (A) = - 4 - 12 - 1 = - 17 We need to find det (2^{2} A) = det (4 A) .For a matrix of order n \times n, det (k A) = k^{n} det (A) .Here, order n = 3 and k = 4 : det (4 A) = 4^{3} det (A) = 64 \times (- 17) = - 1088

Try it yourself before checking the explanation above.

Find the value of det (2^{2} A) for the following matrix: A = 2 - 1 - 3 301122

1340

-1282

-1088

1542

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